This demonstration recreates an example of introspective
training from E.B. Titchener's laboratory manual of 1901-1905. The purpose
is to prompt thought about the prospects of introspective training as a means of
improving the quality of introspective reports about conscious experience.
The demonstration requires speakers or headphones, and a high-speed
internet connection is recommended.

Titchener and most of his contemporaries (circa 1900) regarded introspection as the principal method of psychology.
Nevertheless, they felt that the introspective reports of
untrained subjects are prone to error, even when the reports are restricted to current or very recently past conscious experience. (I share this view:
Schwitzgebel 2002a&b, in preparation; Schwitzgebel & Gordon, 2000.) They
consequently recommended extensive training in introspective procedures. Wilhelm
Wundt, Titchener's teacher and founder of the introspectionist school of
psychology, is reputed not to
have admitted introspective data from observers with fewer than 10,000 trials of
experience in introspective report (Boring 1953).

To assess the merits of classical introspective training techniques, it
would be desirable to train people as the introspective psychologists
recommended. Titchener's vast, four part laboratory manual (1901-1905)
details the methods. While it is not practical to attempt all the
procedures Titchener describes, we may easily run through one example.
Doing so will help reveal both the promise and the problems of
classical introspective training. (For more extensive reflections on these
matters, see Schwitzgebel, in preparation.)

The procedure here will approximately follow the procedure described by Titchener
(1901-1905), vol.
I, part 1, pp. 39-46. The reader will be trained to discern difference tones.

What a Difference Tone Is

When two pure tones are played together, it sometimes sounds as
though a third tone is also present. For example, a person simultaneously
hearing two loud tones of 800 and 1000 hertz may also report hearing another,
quieter tone at about the pitch one would expect from a 200 hz stimulus.
More generally, if two generating tones (or primary tones) of
frequency U (for the upper tone) and L (for the lower tone) are played together,
people will under some conditions report hearing a difference tone (or
first difference tone) that sounds like a tone presented at frequency U - L,
despite the fact that waveform analysis may show no sound wave at that
frequency.

Similarly, people sometimes report hearing, in addition to or
instead of the first difference tone, a second difference tone at
approximately the pitch one would expect from a stimulus of frequency 2L - U
(600 hz, if the generating tones are 800 and1000 hz). Titchener also
describes a third difference tone at 3L - U and a summation tone
at U + L. Other investigators report tones at 3L - 2U, 4L - 3U, 2U - 2L,
3U - 3L, and other frequencies. As a class these are known as combination tones.
In stimuli with prominent overtones (overtones have a frequency that is an integer
multiple of the fundamental frequency of the stimulus, such as 2U, 3U, 4U,
etc.), people sometimes report hearing combination tones arising from the
overtones.

It is generally thought that combination tones are heard as a
result of inefficiencies in the ear.

Adjusting Your Speaker Volume

To prepare yourself to hear difference tones, please increase your speaker or headphone volume to the
maximum
comfortable setting while listening to the following stimulus: volume
test. (If this stimulus is taking a long time to download, cancel the
download and follow the directions in the next section.)

The stimulus should be somewhat unpleasant but not painfully
loud. Listen to it several times to be sure that the volume is as high as
possible without causing pain. I have noticed in previous versions of this
demonstration that people typically do not initially turn the volume high
enough.

If your speakers produce distortion at the required volume
level, decrease the volume and move one ear close to one speaker, or get
headphones, then perform the volume test again. Overdriven amplifiers
produce tones much like the combination tones produced by the ear. Perhaps
it does not matter, from an introspective perspective, whether the tones of
interest are produced by the amplifiers or by the ear -- since ear and air are
equally outside the brain -- but it seems preferable to avoid this complication.

Directions for People with Slow Internet Connections

If the test stimulus took more than a few seconds to download,
you will need to download all the stimuli together as a package, since it is important to access them quickly during the training and tests.
Download this zipfile
into an empty temporary directory, then unzip it. Instead of clicking on the links
in this document, open the files associated with the link. (So, for
example, if the link is "http:// ... [whatever] .../T01.wav", play the
sound file "T01.wav" from your temporary directory.) In Internet Explorer or Mozilla, when you
move the cursor over a link (without clicking), you can see the filename near
the bottom of your screen, if the "status bar" is not hidden.
Unfortunately, the zipfile is large (30 MB) and may take several hours to
download.

Optional Pre-Test and Post-Test

If you wish to take it, an optional pre- and
post-test is available in Appendix A below. Titchener's original procedure
does not involve such a pre- and post-test.

Titchener's Training, Part One

We will now follow approximately the procedure described by
Titchener (1901-1905), vol. I, part 1, pp. 39-46. The most noteworthy
differences between the present procedure and Titchener's are: the optional pre-test and post-test; a more consistent reliance on the multiple-choice
format; the addition of pauses for methodological reflection; and (of course)
the presentation of the tones through the computer. Appendix B contains a
further discussion of some of the procedural details.

Throughout the procedure, note the features of your auditory
experience as much as is practicable without detracting too much from the
central task.For example: Do the
tones seem to change pitch or loudness in the course of presentation?Do you hear more than one combination tone at a time?Does the loudness, or the very presence, of a combination tone vary with
attention?Do the properties of the
tone vary depending on the other tones that are heard or attended to?Is there a “fusion” of tones more for some intervals than
for others?These were some of the
questions that interested Titchener and other early introspective psychologists,
and Titchener generally encouraged his introspective observers to report such details.
(You may forget to reflect on these matters once you are absorbed in the
training, but Titchener collected from his students written introspective
reports that were expected to contain at least a few such details.)

(1.) First, play the tones g3
(the third G above middle-C) and b3
(the third B above middle-C) separately, several times, to accustom yourself to the pitch of the two
generating tones.

Now listen to the two
tones together. In this sample, the g3 plays for 1 second,
then b3 joins it for five seconds.

You should hear at least one tone distinctly lower than either
of the two generating tones. The first difference tone, on which this
training will focus, is two octaves
below the g3 at g1.
(From here forward, the term 'difference tone' should be taken to mean 'first
difference tone' unless otherwise specified.) It may sound a bit like background hum in your speakers
of the sort that you are accustomed to ignore.
Some people, especially those listening at lower speaker volumes, describe this
difference tone as considerably quieter than either of the generating tones;
others find it every bit as loud and salient as the generating tones.
Since the tone is a perfect two octaves below the lower generator, it may also harmoniously "fuse" with that generator to some extent.
Titchener recommends that you listen to the stimulus several times, until you are
"entirely satisfied with [your] introspections" (1901-1905, vol. I,
part 1, p. 41).

If you did not hear the difference tone,
try either increasing the volume on your speakers, switching to headphones, or
reducing background noise. If you still do not hear the difference tone,
you might try listening to g1 at a lower volume, so that its loudness more
closely matches that of the expected difference tone; or you might listen to the
stimulus first at a low
volume (which should make the difference tone inaudible), then at a higher
volume, listening for the addition of a lower pitched tone. If you still feel unable to hear
the difference tone, try listening to the remedial stimuli below (not adapted from Titchener),
which most people find to contain obvious difference tones. If you heard
the difference tone in g3+b3 and you wish to abide closely by
Titchener's presentation, you should skip the remedial tones for now,
though of course you may return to them after the training procedure is
complete.

Optional Interlude: Remedial Stimuli

Remedial difference tone sample 1. Listen to these
two harmonica notes played separately: 7draw,
8draw;
then together: 78draw.
Can you hear a faint tone at this pitch: diff?
(This example and the stimuli are from Pat Missin's website, http://www.patmissin.com/ffaq/q26.html
, accessed December 2002.)

Remedial difference tone sample 2. Here a tone of
1000 hz is played for two seconds, then it is joined by another tone of 1000 hz
that slowly rises to 2000 hz. The difference tone is a low note that
slowly rises to the pitch of the 1000 hz tone: rising.
The second difference tone may also be fairly salient as a tone declining in pitch
about two-thirds of the way through the stimulus. (You may also hear
another declining tone just before the second difference tone becomes salient,
at 3L - 2U, and you may notice a few fluttering
"beats" as the rising tone first joins the steady, 1000 hz tone.)

Remedial difference tone sample 3. Here g3 and b3
are played together, starting very quietly and rising in intensity to the normal
level. You may hear the low difference tone g1
come in as the intensity increases: g3+b3amp.
High tones, like a ringing in the ears, may also be salient near the end of the
stimulus. (These may be due to aural harmonics, summation tones, and/or
amplifier distortion.)

If you heard a difference tone in any of the remedial stimuli,
but not in the g3+b3, please return to that interval again, now that
you have a better sense of what you're looking for. If you still hear no
difference tone, you may not hear any in the remainder of this demonstration.

Titchener's Training, Part Two

Hopefully, you heard a difference tone in g3+b3
above. Now listen again to the stimulus and then to 1A,
1B,
and 1C.
Determine which of these tones is identical to the difference tone. You
may play the stimulus and the options several times if necessary. After
you have settled on a choice, compare it with g1to verify. (Appendix C also contains the
answer, but looking there risks spoiling the training by revealing the
correct responses to questions you have not yet tried.) (If your browser brings up separate windows for each sound
file, you may wish to place the windows next to each other so that you can move
quickly between the sounds presented, thereby minimizing tonal memory requirements. Close the windows
for each tone once you move on to the next part of the training.)

If you have chosen incorrectly, listen to the tones and
intervals again until you feel that you can properly identify the pitch of the difference
tone. Proceed to (2) either when you are confident that you can identify
the pitch of the difference tone or when you judge that further effort would be of little
use.

Throughout the training and post-test you may wish to take occasional breaks, to "cleanse the palate" as it
were.

(2.) The second trial proceeds much as the first. This
time, play the tones g3
and d4
(the fourth D above middle-C),
first separately, then together,
listening for the difference tone. In this case, the difference tone is one octave below the lower generating
tone, at g2.
(This also happens to be the pitch of the second difference tone.)

Now listen to g3+d4
and 2A,
2B,
and 2C.
After determining which of the latter tones is identical to the difference tone, compare with g2
to verify.

As before, if you chose incorrectly, listen to the stimulus and
choices again until you feel you can properly discern the difference tone and
identify its pitch. If you are struggling, you may wish to go back to the
optional section containing the remedial stimuli, if you have not already
listened to those stimuli.

Interlude for Methodological Reflections

Let's pause to consider a few methodological questions before
proceeding. First, what were you attending to in these experiments?
Were you attending to the world -- that is, to the sounds (assuming sounds are
the sort of thing that exist in the world)? Or were you attending to your
("inner" or "conscious") experience? Is there even a
difference between the two sorts of attention?

Suppose that in either (1) or (2), you guessed
"incorrectly" but then became convinced of the "correct"
answer after further listening. Does it seem to you possible that your experience
changed sufficiently in the interval to make both guesses in some sense correct? For example, suppose that you guessed too high at first in (2),
then eventually arrived at the opinion that g2 was indeed the same pitch as the difference tone. Could it be the case that at first your auditory
sensation contained something resembling a difference tone at the higher pitch
but no difference tone at g2, and that the auditory experience
afterward changed, lowering the tone to g2? In other words, the
assumption of the training procedure is that there really are difference tones
of certain pitches in your experience and that you may misapprehend them or fail
to discern them altogether. However, an alternative
possibility is that your description of your experience is always accurate, and
that if your judgment changes, it is only because the experience itself changes.

To what extent does your developing knowledge of difference
tones affect your auditory experience? We may suppose that the experience
prior to training is different from the experience after training, without
necessarily supposing (as in the previous paragraph) that our experience always
marches in step with our judgments about it.

Listening to the second stimulus, g3+d4, I find myself feeling that the
difference tone is a bit higher than the g2, but that the g2 is a closer match
than the next higher pitched option. I am tempted to suggest that the presence of the
higher tones creates a context in which the auditory sensation of the g2
difference tone is higher in pitch that of the g2 sounded alone. On
reflection, however, that thought strikes me as strange. The
"g2" difference tone of course doesn't exist apart from the generating
tones. It is not some independent thing to be "affected"
by them. Perhaps rather than saying that the pitch of the
difference tone is raised by the
presence of the other tones, it would be better simply to say that the pitch of
the difference tone is a bit higher than that of g2? But consider this sound:
g3+d4(+g2),
which is the g3 and the d4, with a bit of g2 added as a third generating
tone. It doesn't seem as though my auditory experience contains both the
true g2 and the difference tone, heard separately, at a slightly higher pitch,
or that it contains any roughness or "beats" of the sort one would
expect listening to two tones of slightly different frequency played together. Maybe the g2 is slightly shifted upward
in your experience to match the pitch of the
difference tone? Maybe the difference tone is lowered by the addition of
the g2, or the two are fused into an intermediate tone? Or perhaps my
introspective judgment that the difference tone is slightly higher in pitch than
g2 is erroneous?

Titchener's Training, Part Three

Below you will find the intervals from the minor 6th through the
octave, along with the associated (first) difference tones and three test tones
for verification. Proceed as before, listening several times to the
stimulus and options if you don't find the answer immediately obvious. Don't be surprised,
however, if some of
the difference tones seem to be inaudible.

You may find yourself, during this series, tempted to adjust the
volume on your computer. Yield to that temptation. It is better to adjust the volume
now than to damage your hearing (of course!) or to fail to hear most of the
difference tones because the generating tones are too quiet (and thus miss the
point of the demonstrations). If you took the pre-test, bear in mind that any adjustment done
now will invalidate the post-test unless you then restore the volume it its
original setting.

(7.) For completeness, listen to the octave g3+g4.
There is no distinct difference tone in this case, since it would be identical
to the g3.

More Methodological Reflections

If you can't discern a difference tone in one of the
stimuli, does it follow that there is no such tone in your experience? At
least three possibilities beckon: (A.) The difference tone is genuinely a
distinct part of your experience, but you have not (yet) succeeded in discerning
it. (B.) The difference tone contributes in some way to your overall
experience, but not in such a way as to be separately discernible, even in
principle. (C.) The difference tone is no respect part of your experience.

Even if you guess correctly on a particular stimulus,
it doesn't follow that the
difference tone is a separately discernible part of your experience. You
may pick out the right answer simply because that tone somehow, perhaps ineffably, fits
with the experience of the stimulus in the way the others do not; or you might
be gaining a sense of the pattern of rising pitch in the difference
tones and thus know where to expect one.

Perhaps you feel that you hear a combination tone in
one of these cases, but you cannot reliably identify it with any of the three
associated options. Should you trust your judgment that you experience the
tone? Is it a question of tonal memory? Do you think you would similarly have trouble picking one tone out
of a chord of three? If you're curious about the last question, try the
following test. A tone will be presented for one second, then it will be
joined by both a higher and a lower tone for five seconds. The lower tone
will be 0.5% of the intensity of the other two (23 decibels less intense), and
its pitch will not be in vicinity of either the first or the second difference
tones of the two higher tones. Try to determine the pitch of the lower
tone. Chord.
ChA,
ChB,
ChC.
You may be distracted by one or another of the combination tones, so feel free to
play the chord again, listening for something in the range of the three
options. Key.

What if you reliably guess the "wrong" tone
for one of the intervals, and after repeated verifications, you still feel that
that is the genuine pitch of the difference tone for you? Could you be
mistaken in this?

Titchener's Training, Part Four

Now try the intervals from the tri-tone down to the semitone (excluding the major third, which was presented in (1)). Do not listen to
the key until you have chosen from among the three options. The difference tones in this series
are lower and farther apart, so the options will each be a major whole tone removed
from each other, rather than a semitone as in the previous series.

So far, the pitch and the order of presentation of the stimuli
has followed Titchener. At this point in the text, however, Titchener
recommends that his introspectors-in-training practice hearing the difference
tone when the sound intensity is slight, when the generating tones differ
substantially in intensity, and when their duration is short. He does not
specify any particular tone intervals, sound intensities, or durations. We will
practice briefly with three stimuli in each category, varying the frequency of the
generating tones within Titchener's scale. In these exercises, as in the
preceding ones, you may wish to listen to the stimulus more than once before
guessing.

Here are three stimuli in which the intensity of the higher of
the generating tones is 30% of the intensity of the lower generator. As in
previous practice, if you guess incorrectly in these exercises, listen to the
stimuli and alternatives again.

Now try three stimuli in which both generating tones are at 30% of the
standard intensity. If you're having trouble hearing a difference tone
at first, try bringing the speaker a little closer to your ears. Then resume normal position and assess whether you
can still hear it.

Titchener continues training with the second difference tone,
the third difference tone, and the summation tone, but
rather than introducing an extensive training series for any of these, I will
provide three examples of the second difference tone, then conclude the
demonstration.

(22.) g3+f-sharp4.
22A,
22B,
22C.
Key.
This is the same stimulus as in (6). Some people find the low second difference tone more salient than the first
difference tone, which is similar in pitch to the lower generating
tone. Titchener again recommends that the experiment be repeated
"until [the observer] is satisfied with his introspections"
(1901-1905, vol. I, part 1, p. 43). Can you hear both the first and the
second difference tones?

If you feel that you can hear the second difference tones in any
of the stimuli, consider this: Are second difference tones qualitatively any
different from first difference tones, apart from differences in pitch?

For fun, listen to this
song. Can you hear this
tune in the difference tones? You may also find it interesting to
determine how many combination tones you can hear in what was presented above as
the second remedial stimulus, a 1000 hz tone joined by another tone rising from
1000 to 2000 hz: rising.
(The audibility of combination tones in this range is discussed in Plomp 1965,
1976.)

Optional Post-Test:

If you took the optional pre-test, return now to
Appendix A and follow the instructions for the post-test. Even if you
didn't take the pre-test, you may want to take the post-test if you wish to hear
some challenging stimuli.

Concluding Discussion:

Let's suppose that you felt more competent in discerning
combination tones at the end of the training than at the beginning and furthermore that
this feeling of competence is well justified. The question then arises: What
exactly have you learned?

Titchener would say that you have improved your ability to
introspect your auditory experience. Perhaps it is also correct to say
that you have been musically trained, trained perceptually, to respond in
certain ways to environmental stimuli. It would seem that there is a
difference between these two types of training: In introspective training, you
learn to discern features of your own experience, while in perceptual training
you learn to discern features of the environment. Yet here, the
two types of training seem to collapse together. Were you attending to the
environment or to your auditory experiences in the training and test?
Psychoacousticians and music teachers sometimes train people in "analytic
listening" -- that is, in picking individual tones out of a complex
stimulus. They don't typically frame such a task as introspective, but one
may wonder: Is the training procedure above really different in kind from that?

Regardless how one resolves such difficulties, however, let me
suggest that you have been introspectively trained in at least the following
respect. Your ability to parse and analyze your auditory experience has
improved. Prior to training, if you had been presented with g3+f4, say,
and then asked whether you simultaneously had an auditory experience of a tone at f1 (while hearing a
sample of that tone), you would have denied it; now you would affirm it. Surely the Gestalt psychologists were
right to say that Titchenerian analysis of experience into distinct elements
distorts the experience, and that experience prior to training and experience
after training cannot be assumed to be the same. Nonetheless, if there is
any sense in which the f1 was an aspect of your experience prior to training,
you are now attuned to it in a way you were not before. Given the rich
complexity of most auditory experience, it seems plausible to suppose that most
people can parse it only very roughly. Now, perhaps, you can parse it just
a little better.

There were many reasons for the death of classical introspective
training: Gestalt psychologists raised legitimate concerns and objections that
were somewhat overplayed; the classical introspective psychology
research program yielded few socially valuable results and bogged down in sterile
debates; behaviorism and functional psychology offered exciting and seemingly
much more useful research prospects. But also, most people found introspective
training techniques of this sort tiresome, as has been emphasized by
Titchener's student and the great historian of psychology, the unfortunately but
in this context aptly named E.G. Boring (1953). Maybe an hour and a half with this
demonstration is okay, but can you imagine enduring 10,000 introspective
trials? Still, if we wish seriously to study conscious experience, it
would seem that some researchers, at least, should develop skill at parsing
particular aspects of their experience and recognizing features of it -- and
that this skill should be recognized as a kind of introspective acumen.
The time is ripe for a
limited resuscitation of the techniques of classical introspective training.

To help you assess whether you have learned anything from the
training procedure, I have provided a short optional pre-test and
post-test. The questions on this test are intended to be difficult to
answer without training, so do not be discouraged if you get them wrong.
Also, feel free at any time to skip forward to the training section.

Here is a sample of the pre-test procedure. First, listen to this Sample
Test Stimulus twice. Then decide this: Did you hear in the test
stimulus a tone of approximately this pitch: Sample
Option A? You may listen to this option twice, if
necessary. Did you hear a tone of approximately this pitch: Sample
Option B? You may also listen to this option twice if necessary. In
answering these questions, do not go back and listen to the test stimulus
again. (In this example, you should have answered "no" to both
questions.)

All the test stimuli consist of one tone played for one second,
joined by a second, higher tone for five seconds. The options will always
tones be lower in pitch than either of the two primary tones in the stimulus. If
you hear those tones at all in the test stimulus, they will likely seem to be much quieter than the two
primary tones.

You may hear in the test stimulus a tone at either of the two options, at both, or at
neither. Do not guess randomly. Since you will only be listening to
three test stimuli in the pretest, a couple of lucky guesses could lead to a
false impression of competence. Most untrained listeners will not be able
reliably to discern a lower tone in any of the test stimuli.

To start the pretest, choose one of the test stimuli from
Group I below, listening for a quiet tone lower in pitch than either of
the two primary tones. Play the chosen test stimulus twice, then listen
to the two associated options without returning to the test stimulus.

Group I (choose only one of the three test stimuli):

Test
Stimulus 1. Try not to be too distracted by the fluttering
"beats". Did you hear a tone of approximately the pitch of Option
1A? Option
1B? (Option 1A is very low, and you may not hear it at low or
intermediate speaker volumes.)

Once you have decided whether you heard a tone at Option A,
Option B, both, or neither, listen to whichever of the following
"keys" matches the test stimulus you chose: Key
for Test Stimulus 1; Key
for Test Stimulus 2; Key
for Test Stimulus 3. The key plays the "right" answer.
If a moderately practiced ear would discern one of the two option tones in the
test stimulus, the key will play that tone. If it would discern both tones,
the key will play both; if neither, the key will be silent. Please note now which
of the three stimuli you chose and whether you were successfully able to discern
the lower tone or tones, if any. Do not listen to the other two test
stimuli in Group I: You will be asked to listen to them as part of the post-test.

Follow the same
procedure for the next two groups of test stimuli. Chose one test stimulus
from each group, listen to it twice, then quickly play the options and determine
whether you heard a tone at one, both, or neither of the two pitches.
Finally, listen to the key. Bear in mind that you may hear a combination tone
that is not among the two options (in which case the correct answer is
"neither".)

A few people, even without any specific training in hearing
difference tones, find the pre-test easy. If you are among those people,
try the following more challenging stimuli. If you found the pre-test
challenging or impossible, skip these stimuli. You may listen to them
after the training if you wish.

I
have not constructed a more challenging post-test, but you may return to these
three stimuli after the training to determine whether you feel any more
comfortable with them.

Post-Test Instructions

Since the perceived loudness of difference tones varies
substantially with relatively small changes in the intensity of the generating
tones, it is important that the stimuli of the post-test not be more intense than
those of the pre-test. If you turned your speakers up during training,
turn them back down. If you are in the habit of pressing the headphones
against your ears to hear better, drop that habit if it was not already in
place during the pre-test. Improved performance on the post-test should
not be attributable to increased stimulus intensity.

If you have picked up a habit such as humming, you may wish to
drop that habit. The same might apply to more "internal" habits,
such as silently maintaining an auditory image of the difference tone (hearing
it as one might hear a tune "in one's head") or attempting consciously
to determine where a difference tone may be expected -- although it is difficult
to draw a line between cognitive habits acquired during training that should be
regarded as legitimate features of introspective expertise and those that should
be regarded as non-introspective crutches.

Stimuli will vary
considerably in pitch and interval, and the keys may be selected from any of
several possible combination tones, to disrupt simple pattern recognition
strategies.

The same stimuli are presented below that were presented in the
pre-test. Listen first to the stimuli that you did not choose for
the pre-test. As in the pre-test, listen to each stimulus only twice and do
not listen again to the stimulus while attempting to answer the question.
You may also listen to the options twice if you wish.
Recall that one option may key, or both or neither. Do not play
the key until you have decided whether you hear a combination tone at either,
both, or none of the frequencies. As in the pre-test, do not guess
randomly. You may listen to the stimuli you selected in the pre-test after
you have listened to all the other stimuli.

Standard, contemporary, psychophysical procedures cannot be followed in this
presentation. It is not, for example, possible to control
properly for background noise, speaker distortion, or sound pressure level.
Despite these shortcomings, however, the training can produce interesting results. The main purpose, recall, is not to establish any particular
psychophysical claim but rather to prompt thought about the nature and prospects
of introspective training.

All the tones presented are simple sine waves, without
overtones, generated by
Cool Edit 2000 Lite, version 1.1. Durations are accurate to .03
seconds. Titchener states that combination tones are easier to hear
without the distraction of overtones (1901-1905, vol. 1, part 2, p. 72), and
recommended Quincke's tubes in part for this reason.

The training procedure follows Titchener in using a just
intonation scale based in C-major (with the A above middle C at 440 hertz) for
the generating tones, rather than the musically standard equal temperament
scale. In just intonation, the ratios of the frequencies of the different
notes are relatively simple fractions, but the transposition of a song into a
different key is not possible without retuning. Titchener suggests that
combination tones are easier to hear the more closely the generators approach just intonation vibration ratios (ibid.).
Titchener
(1901-1905), vol. I, part 1, p. 32, lists the just intonations for the natural
tones. To resolve ambiguities regarding the
intonation of sharps and flats, I referred to Rossing, Moore, and Wheeler (2002).

In Titchener's notation,
middle C is 'c1', the C above that is 'c2', and so forth (omitting the
superscript). One octave below middle C is lower-case 'c'; one octave below that,
capital 'C'; then
'C1'
and so forth (omitting the subscript). Notes other than C take the format of the C below them
(thus, the A above middle C is 'a1' and the A below it is 'a').
Titchener's scale and notation are described in vol. I, part 1, pp. 32-33.
(Thus, Titchener's c1 is approximately the standard C4 in contemporary equal
temperament notations.)

Much of the training uses g3 as the lower generator. Since
I abide by Titchener's just intonation scale for C-major, the
tri-tone is a bit sharp (in (8)) and the major whole tone a bit flat (in (11)) relative to the standard
just intonation vibration ratios for those intervals.

When a multiple choice is offered, the tones presented
are either separated by exactly a semitone (for tones over 900 hz) or
exactly a major whole tone (for tones below 900 hz), in just intonation, although that
typically takes the
tones slightly off Titchener's scale. (Note that in just intonation, two
semitones (16/15 ratio) do not constitute a major whole tone (9/8 ratio), nor do two major
whole tones constitute a major 3rd (5/4 ratio).) If the pitch of the predicted difference
tone does not precisely match that of the tones in Titchener's scale,
the exact predicted difference tone is nonetheless presented. The
predicted difference tone is equally likely to be the highest, the lowest, or
the middle tone (except when confusion might result from approximating the pitch of another salient combination tone), and the order of the tones
is randomized.

Note: For the test stimuli, the distractor is chosen so as not
to be within a major 3rd of any combination tone of the form nU + mL, when n and
m are integers from -5 to 5. (Exceptions are Test 11, where the distractor
is a major 2nd lower than the key and a major 2nd higher than the fourth
difference tone (4L - U), and Test 12, where due to the moderate pitch of the
summation tone and the low frequency of the generators, it is impossible to avoid
being within a major 3rd of some of the more obscure combinations, such as 3U -
2L.)

Here are the generator tones for the difference tone song
(Scarborough Fair):

Titchener, E.B. (1901-1905). Experimental psychology: A
manual of laboratory practice. London: MacMillan. [Note:
Titchener's two volumes are each divided into student's and instructor's parts,
published under separate covers. The widely available 1971 reprint omits
the instructor's part of the first volume.]